Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session Q7: Multiphase Flows: Computational Methods IICFD Multiphase

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Chair: Khosro Shahbazi, South Dakota School of Mines and Technology Room: 407 
Tuesday, November 21, 2017 12:50PM  1:03PM 
Q7.00001: Formulating a subgridscale breakup model for microbubble generation from interfacial collisions Wai Hong Ronald Chan, Shahab Mirjalili, Javier Urzay, Ali Mani, Parviz Moin Multiphase flows often involve impact events that engender important effects like the generation of a myriad of tiny bubbles that are subsequently transported in large liquid bodies. These impact events are created by largescale phenomena like breaking waves on ocean surfaces, and often involve the relative approach of liquid surfaces. This relative motion generates continuously shrinking length scales as the entrapped gas layer thins and eventually breaks up into microbubbles. The treatment of this disparity in length scales is computationally challenging. In this presentation, a framework is presented that addresses a subgridscale (SGS) model aimed at capturing the process of microbubble generation. This work sets up the components in an overarching volumeoffluid (VoF) toolset and investigates the analytical foundations of an SGS model for describing the breakup of a thin air film trapped between two approaching water bodies in a physical regime corresponding to Mesler entrainment. Constituents of the SGS model, such as the identification of impact events and the accurate computation of the local characteristic curvature in a VoFbased architecture, and the treatment of the air layer breakup, are discussed and illustrated in simplified scenarios. Supported by ONR/A*STAR. [Preview Abstract] 
Tuesday, November 21, 2017 1:03PM  1:16PM 
Q7.00002: Modeling Subgrid Scale Droplet Deposition in MultiphaseCFD Giulia Agostinelli, Emilio Baglietto The development of firstprinciplebased constitutive equations for the EulerianEulerian CFD modeling of annular flow is a major priority to extend the applicability of multiphase CFD (MCFD) across all twophase flow regimes. Two key mechanisms need to be incorporated in the MCFD framework, the entrainment of droplets from the liquid film, and their deposition. Here we focus first on the aspect of deposition leveraging a separate effects approach. Current twofield methods in MCFD do not include appropriate local closures to describe the deposition of droplets in annular flow conditions. As many integral correlations for deposition have been proposed for lumped parameters methods applications, few attempts exist in literature to extend their applicability to CFD simulations. The integral nature of the approach limits its applicability to fully developed flow conditions, without geometrical or flow variations, therefore negating the scope of CFD application. A new approach is proposed here that leverages local quantities to predict the subgridscale deposition rate. The methodology is first tested into a threefield approach CFD model. [Preview Abstract] 
Tuesday, November 21, 2017 1:16PM  1:29PM 
Q7.00003: LES of stratifiedwavy flows using novel nearinterface treatment Aditya Karnik, Lyes Kahouadji, Jalel Chergui, Damir Juric, Seungwon Shin, Omar K. Matar The pressure drop in horizontal stratified wavy flows is influenced by interfacial shear stress. The nearinterface behavior of the lighter phase is akin to that near a moving wall. We employ a fronttracking code, {\it Blue}, to simulate and capture the nearinterface behaviour of both phases. {\it Blue} uses a modified Smagorinsky LES model incorporating a novel nearinterface treatment for the subgrid viscosity, which is influenced by damping due to the walllike interface, and enhancement of the turbulent kinetic energy (TKE) due to the interfacial waves. Simulations are carried out for both airwater and oilwater stratified configurations to demonstrate the applicability of the present method. The mean velocities and tangential Reynolds stresses are compared with experiments for both configurations. At the higher Re, the waves penetrate well into the buffer region of the boundary layer above the interface thus altering its dynamics. Previous attempts to capture the secondary structures associated with such flows using RANS or standard LES methodologies have been unsuccessful. The ability of the present method to reproduce these structures is due to the correct estimation of the nearinterface TKE governing energy transfer from the normal to tangential directions. [Preview Abstract] 
Tuesday, November 21, 2017 1:29PM  1:42PM 
Q7.00004: A hybrid interface trackinglevel set technique for multiphase flow with soluble surfactant in Blue Omar K. Matar, Seungwon Shin, Jalel Chergui, Damir Juric, Lyes Kahouadji, Richard V. Craster We adapt a formulation for surfactant transport in multiphase flows presented by Muradoglu \& Tryggvason (JCP 274 (2014) 737757) to the context of the Level Contour Reconstruction Method (Shin {\it et al}. IJNMF 60 (2009) 753778), a hybrid method that combines the fronttracking and levelset methods. Attention is paid to the formulation and numerical implementation of the surface gradients of surfactant concentration and surface tension. Various benchmark tests are performed to demonstrate the accuracy of different elements of the algorithm. To verify surfactant mass conservation, values for surfactant diffusion along the interface are compared with the exact solution for the problem of uniform expansion of a sphere. The numerical implementation of the discontinuous boundary condition for the source term in the bulk concentration is compared with the approximate solution. Surface tension forces are tested for Marangoni drop translation. Our numerical results for drop deformation in simple shear are compared with previous experimental and numerical results yielding good agreement. We also demonstrate that our approach applies easily to massivelyparallel simulations. [Preview Abstract] 
Tuesday, November 21, 2017 1:42PM  1:55PM 
Q7.00005: Numerical modelling of multiphase liquidvaporgas flows with interfaces and cavitation Marica Pelanti We are interested in the simulation of multiphase flows where the dynamical appearance of vapor cavities and evaporation fronts in a liquid is coupled to the dynamics of a third noncondensable gaseous phase. We describe these flows by a singlevelocity threephase compressible flow model composed of the phasic mass and total energy equations, the volume fraction equations, and the mixture momentum equation. The model includes stiff mechanical and thermal relaxation source terms for all the phases, and chemical relaxation terms to describe mass transfer between the liquid and vapor phases of the species that may undergo transition. The flow equations are solved by a mixtureenergyconsistent finite volume wave propagation scheme, combined with simple and robust procedures for the treatment of the stiff relaxation terms. An analytical study of the characteristic wave speeds of the hierarchy of relaxed models associated to the parent model system is also presented. We show several numerical experiments, including twodimensional simulations of underwater explosive phenomena where highly pressurized gases trigger cavitation processes close to a rigid surface or to a free surface. [Preview Abstract] 
Tuesday, November 21, 2017 1:55PM  2:08PM 
Q7.00006: Highfidelity droplet and bubble simulations using local enrichment Florian Kummer We are going to present a highorder numerical method for multiphase flow problems, such as droplets or bubbles, which employs a sharp interface representation by a levelset and an extended discontinuous Galerkin (XDG) discretization for the flow properties. The shape of the XDG basis functions is dynamically adapted to the position of the fluid interface, so that the spatial approximation space can represent jumps in pressure and kinks in velocity accurately. By this approach, the `$h^p$convergence' property of the classical discontinuous Galerkin (DG) method can be preserved for the lowregularity, discontinuous solutions, such as those appearing in multiphase flows. In realistic droplet setups one observes length scales which may cover several magnitudes. Therefore, in addition to the XDGenrichment one also requires adaptive mesh adaptation. This refinement is featurebased, i.e. controlled by the local curvature. Our presentation will focus on some of the critical buildingblocks of the method and their integration in the full solver. [Preview Abstract] 
Tuesday, November 21, 2017 2:08PM  2:21PM 
Q7.00007: An Interpolative ParticleLevel Set Method for Interfacial Physics Lindsay Crowl Erickson, Jeremy Templeton, Karla Morris We present a novel hybrid particle level set method for solving multiphase flow problems involving moving interfacial dynamics. Our method incorporates the advantages of a Lagrangian particle approach to correct errors due to numerical diffusion in the level set equation and resolve spatial inhomogeneity at a finer scale than is attainable from the background mesh on which the Eulerian level set equation is solved on. We propose a new interpolative particle level set method that uses a (bi/tri) linear interpolation scheme to correct the level set field near the interface in a smooth fashion and uses all nearby particles instead of just escaped particles. Our results show that this method can outperform the original particle level set method by retaining a smooth corrected level set field near the interface and requiring fewer Lagrangian marker particles per grid cell in the correction procedure. [Preview Abstract] 
Tuesday, November 21, 2017 2:21PM  2:34PM 
Q7.00008: multiUQ: An intrusive uncertainty quantification tool for gasliquid multiphase flows Brian Turnquist, Mark Owkes Uncertainty quantification (UQ) can improve our understanding of the sensitivity of gasliquid multiphase flows to variability about inflow conditions and fluid properties, creating a valuable tool for engineers. While nonintrusive UQ methods (e.g., Monte Carlo) are simple and robust, the cost associated with these techniques can render them unrealistic. In contrast, intrusive UQ techniques modify the governing equations by replacing deterministic variables with stochastic variables, adding complexity, but making UQ cost effective. Our numerical framework, called multiUQ, introduces an intrusive UQ approach for gasliquid flows, leveraging a polynomial chaos expansion of the stochastic variables: density, momentum, pressure, viscosity, and surface tension. The gasliquid interface is captured using a conservative level set approach, including a modified reinitialization equation which is robust and quadrature free. A leastsquares method is leveraged to compute the stochastic interface normal and curvature needed in the continuum surface force method for surface tension. The solver is tested by applying uncertainty to one or two variables and verifying results against the Monte Carlo approach. [Preview Abstract] 
Tuesday, November 21, 2017 2:34PM  2:47PM 
Q7.00009: Dynamic Mode Decomposition of a Numeric Simulation of a Jet in Crossflow William Krolick, Mark Owkes Numerical methods have advanced to the point that many groups can perform detailed numerical simulations of atomizing liquid jets and replicate experimental measurements. However, the simulation results have not lead to a substantial advancement to our understanding of these flows due to the massive amount of data produced. In this work, we develop a tool to extract the physics that destabilize the jet’s liquid core by leveraging dynamic mode decomposition (DMD). DMD takes ideas from the Arnoldi method as well as the Koopman method to evaluate a nonlinear system with a low rank linear operator. The method is beneficial to us in that it reduces the order of the simulation results from all the original data through time to a few key pieces of information. Most important of these are the dynamic modes, their time dynamics, and the DMD spectra. In this case, DMD is applied to the jet’s liquid core outer radius, which is computed at streamwise and azimuthal locations, i.e., $R(x, \theta)$. With the DMD data, we obtain the dominant spatial and temporal modes of the system and their stabilities. The dominant modes provide a useful way to collapse the large dataset produced by the simulation into a length and timescale that can be used to initiate reducedorder models. [Preview Abstract] 
Tuesday, November 21, 2017 2:47PM  3:00PM 
Q7.00010: Positivitypreserving finite difference schemes for robust computations of multicomponent flows Khosro Shahbazi The positivitypreserving property is of paramount importance in design of numerical schemes considering that violation of positivity not only yields unphysical solutions, but also causes the computation to fail (numerical codes crash) due to the appearance of complex (nonreal) characteristic speed. While the positivity enforcement in the singlephase flow context has gained significant development in recent years, hardly any research has been focused on compressible multiphase flows involving shock wave bubble interactions ; with an exception being my own recent work using finite volume schemes, (Journal of Computational Physics (2017) 339 163179). This is due to increased complexity of the multiphase flow models and the fact that, unlike in singlephase flow model, in the multiphase flow model the pressure function is no longer a concave function of the conservative variables, a property often exploited for the design of positivity scheme in the single phase flows. Therefore, in this talk I present the development, analysis and verification of an original highorder positivitypreserving finite difference scheme for robust twocomponent flow computations. The positivity enforcement is based on a minimal limiting of the highorder numerical fluxes toward the firstorder monotone fluxes such that the density, modified pressure and order parameters, identifying each phase's transport, fall within the acceptable physical bounds. Compared to highorder finite volume counterpart, the proposed highorder finite difference schemes are easier to implement and are computationally less demanding. [Preview Abstract] 
Tuesday, November 21, 2017 3:00PM  3:13PM 
Q7.00011: Simple SecondOrder Finite Differences for Elliptic PDEs with Discontinuous Coefficients and Interfaces ChungNan Tzou, Samuel Stechmann Many multiphase flow problems require the solution of Poisson's equation with discontinuous coefficients due to different fluid properties, such as density, in the different phases of the fluid. Here we present a secondorderaccurate numerical method for this problem, where the method is based on simple finite difference formulas. The derivation is performed on a Cartesian grid and leads to a symmetric operator, even across the interface, with suitable adjustments of the righthand side arising in the derivation and accounting for the interface. The righthand side is then determined using an iterative method. Comparisons with other methods, such as the firstorder ghost fluid method and the secondorder immersed interface method, will be discussed; for instance, the present method does not require derivatives of jump conditions. This numerical method is mathematically proven to be secondorder accurate in one dimension, in which case iterations are not needed. Secondorder accuracy is demonstrated via numerical trials in both two and three dimensions. [Preview Abstract] 
Tuesday, November 21, 2017 3:13PM  3:26PM 
Q7.00012: Boundedness proof for a conservative phasefield method discretized by central finite differences Shahab Mirjalili, Christopher Ivey, Ali Mani It is well known that standard secondorder finite differences have desirable conservation properties that are attractive for DNS and LES. However, when it comes to twophase flow calculations, central differences have often been avoided for the advection operators due to dispersion errors that can lead to boundedness issues and unphysical values for fluid density. We will demonstrate that for a certain conservative phase field equation, given by a second order PDE similar to that of Chiu and Lin (JCP, 2011), it is possible to employ central finite differences and preserve the boundedness of the phase field between the extrema values set at the pure phases. By means of a discrete asymptotic analysis, we will show that the phase field is bounded in a certain region of the discretization parameters space, in which one should operate. When coupled to a finitedifference discretization of the twophase momentum equation, the resulting method emerges as a viable alternative for twophase flow calculations given its ease of implementation, parallelizability, low cost, accuracy, conservation and boundedness properties. [Preview Abstract] 
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